Auckland scientists have made a world-first discovery, sighting complete specimens of the world's rarest whale for the first time.

And they didn't find just one spade-toothed beaked whale, but two, confirming the species still exists.

The pair, a mother and her calf, were seen by scientists when they stranded on Opape Beach in the Bay of Plenty in December 2010. The whales later died.

See a diagram of the whale and where it was sighted here

Lead scientist at Auckland University Rochelle Constantine said they were initially mis-identified as Gray's beaked whales - a more common whale to wash up on New Zealand shores.

The Department of Conservation measured the 5.3m female and her 3.5m male calf and took tissue samples, but genetic analysis at Auckland University revealed they were actually spade-toothed beaked whales.

Auckland University researchers confirmed the species after studying three skull fragments found around New Zealand and Robinson Crusoe Island in Chile.

Fragments were first discovered in the Chatham Islands in 1872, but scientists didn't begin studying them until 2002.

Analysing the fragments, they realised the genetic profiles from each fragment were the same, but did not correspond to any other known species.

Constantine said there was sufficient DNA evidence to confirm they were the bones of the spade-toothed beaked whale, but up until the pair washed onto the beach it was unknown whether they still existed.

The discovery was published today in international journal Current Biology.

Because the pair which stranded in 2010 were the only two whales of the species to ever be seen, they are considered to be the rarest in the world.

"It's incredible to think that, until recently, such a large animal was concealed in the South Pacific Ocean and shows how little we know about ocean biodiversity," Constantine said.

Following the genetic identification of the whales their skeletal remains were exhumed, with the permission of Whakatohea Iwi Maori Trust and the Ngai Tama Haua hapu, and taken to the Museum of New Zealand Te Papa Tongarewa.